def test_dagger():
i, j, n, m = symbols('i,j,n,m')
assert Dagger(1) == 1
assert Dagger(1.0) == 1.0
assert Dagger(2 * I) == -2 * I
assert Dagger(Rational(1, 2) * I / 3.0) == -Rational(1, 2) * I / 3.0
assert Dagger(BKet([n])) == BBra([n])
assert Dagger(B(0)) == Bd(0)
assert Dagger(Bd(0)) == B(0)
assert Dagger(B(n)) == Bd(n)
assert Dagger(Bd(n)) == B(n)
assert Dagger(B(0) + B(1)) == Bd(0) + Bd(1)
assert Dagger(n * m) == Dagger(n) * Dagger(m) # n, m commute
assert Dagger(B(n) * B(m)) == Bd(m) * Bd(n)
assert Dagger(B(n)**10) == Dagger(B(n))**10
def test_commutation():
n, m = symbols("n m", above_fermi=True)
c = Commutator(B(0), Bd(0))
assert c == 1
c = Commutator(Bd(0), B(0))
assert c == -1
c = Commutator(B(n), Bd(0))
assert c == KroneckerDelta(n, 0)
c = Commutator(B(0), Bd(0))
e = simplify(apply_operators(c * BKet([n])))
assert e == BKet([n])
c = Commutator(B(0), B(1))
e = simplify(apply_operators(c * BKet([n, m])))
assert e == 0
c = Commutator(F(m), Fd(m))
assert c == +1 - 2 * NO(Fd(m) * F(m))
c = Commutator(Fd(m), F(m))
assert c == -1 + 2 * NO(Fd(m) * F(m))
C = Commutator
X, Y, Z = symbols('XYZ', commutative=False)
assert C(C(X, Y), Z) != 0
assert C(C(X, Z), Y) != 0
assert C(Y, C(X, Z)) != 0
# assert (C(C(Y,Z),X).eval_nested() + C(C(Z,X),Y).eval_nested() + C(C(X,Y),Z).eval_nested()) == 0
# assert (C(X,C(Y,Z)).eval_nested() + C(Y,C(Z,X)).eval_nested() + C(Z,C(X,Y)).eval_nested()) == 0
i, j, k, l = symbols('ijkl', below_fermi=True)
a, b, c, d = symbols('abcd', above_fermi=True)
p, q, r, s = symbols('pqrs')
D = KroneckerDelta
assert C(Fd(a), F(i)) == -2 * NO(F(i) * Fd(a))
assert C(Fd(j), NO(Fd(a) * F(i))).doit() == -D(j, i) * Fd(a)
assert C(Fd(a) * F(i), Fd(b) * F(j)).doit() == 0
def test_dagger():
i, j, n, m = symbols("i,j,n,m")
assert Dagger(1) == 1
assert Dagger(1.0) == 1.0
assert Dagger(2 * I) == -2 * I
assert Dagger(S.Half * I / 3.0) == I * Rational(-1, 2) / 3.0
assert Dagger(BKet([n])) == BBra([n])
assert Dagger(B(0)) == Bd(0)
assert Dagger(Bd(0)) == B(0)
assert Dagger(B(n)) == Bd(n)
assert Dagger(Bd(n)) == B(n)
assert Dagger(B(0) + B(1)) == Bd(0) + Bd(1)
assert Dagger(n * m) == Dagger(n) * Dagger(m) # n, m commute
assert Dagger(B(n) * B(m)) == Bd(m) * Bd(n)
assert Dagger(B(n) ** 10) == Dagger(B(n)) ** 10
assert Dagger("a") == Dagger(Symbol("a"))
assert Dagger(Dagger("a")) == Symbol("a")
def test_number_operator():
n = symbols("n")
o = Bd(0) * B(0)
e = apply_operators(o * BKet([n]))
assert e == n * BKet([n])
def test_complex_apply():
n, m = symbols("n,m")
o = Bd(0) * B(0) * Bd(1) * B(0)
e = apply_operators(o * BKet([n, m]))
answer = sqrt(n) * sqrt(m + 1) * (-1 + n) * BKet([-1 + n, 1 + m])
assert expand(e) == expand(answer)
def test_basic_apply():
n = symbols("n")
e = B(0) * BKet([n])
assert apply_operators(e) == sqrt(n) * BKet([n - 1])
e = Bd(0) * BKet([n])
assert apply_operators(e) == sqrt(n + 1) * BKet([n + 1])